Would you have

survived the

sinking of the

Titanic?

Presented by Dr. Neil W. Polhemus

Using the Statgraphics mosaic charts, multiple correspondence analysis and logistic regression procedures.

RMS Titanic

Sinking of the Titanic

• Struck an iceberg on April 14, 1912 and sank the

next morning.

• Carried over 2000 passengers and crew, many

of whom did not survive.

• Controversies have centered on the lack of

sufficient lifeboats and the differential treatment

of individuals based on class of accommodation.

Sample Data File #1

Source: Robert J. MacG. Dawson, Saint Mary’s University http://www.amstat.org/publications/jse/datasets/titanic.txt

VARIABLE DESCRIPTIONS: Class (1 = first, 2 = second, 3 = third, 0 = crew) Age (1 = adult, 0 = child) Sex (1 = male, 0 = female) Survived (1 = yes, 0 = no)

n=2,201 observations (all people at risk)

Sample Data File #2

Source: Frank Harrell and Thomas Cason, University of Virginia http://biostat.mc.vanderbilt.edu/twiki/pub/Main/DataSets/titanic.html

n=1,309 observations (passengers only) Note that age is numeric.

Crosstabulation

Mosaic Charts

Mosaic Charts

Mosaic Charts

Mosaic Charts

Multiple Correspondence Analysis

• Creates a map of the associations amongst the

categories of 2 or more variables.

• Seeks a small number of dimensions that

describe most of the variability or “inertia”

amongst the categories.

• Very useful in demonstrating the

interrelationships amongst the variables.

Data Input

Burt Table

Multiple Mosaic Plot

Inertia and Chi-Square Decomposition

Scree Plot

Correspondence Map

Logistic Regression

• Binary logistic regression is designed to model situations in which there are only 2 possible outcomes, such as “survived” or “did not survive”.

• It estimates a model that predicts the probability of those outcomes as a function of 1 or more predictor variables.

• The predictor variables may be either quantitative or categorical.

Bernoulli Events

• A Bernoulli event is an event in which 2

outcomes are possible.

• Let Yi = 1 if ith person survived, 0 otherwise.

• The pmf for a Bernoulli event is

𝑃𝑟𝑜𝑏 𝑦 = 𝑝𝑦(1 − 𝑝)1−𝑦 where 0 ≤ p ≤ 1

Predictor Variables

• We now want to let p be a function of one or

more predictor variables X. In particular:

– X1 = class

– X2 = age

– X3 = sex

Then: 𝑝 = 𝑓(𝑋1, 𝑋2, 𝑋3)

Logistic Model

• When modeling p, we need a model that remains between 0 and 1.

• Most common choice is the logistic model:

log𝑝

1 − 𝑝= 𝛽0 + 𝛽1𝑋1 + 𝛽2𝑋2 + ⋯

• It is a model for the log odds. If less than 0, odds are against the event. If greater than 0, odds are in favor of the event.

Data Input

Analysis Options

Likelihood Ratio Test

• Full second order model

• Simplified model

Plot of Fitted Model

Predictions

Recommended Reading

• Correspondence Analysis in Practice (second

edition) by Michael Greenacre (Chapman and

Hall, 2007)

• Applied Logistic Regression (third edition) by

David Hosmer and Stanley Lemeshow (Wiley,

2013)

Recorded Webinar

• You may find the recorded webinar, PowerPoint

slides and sample data at:

www.statgraphics.com

• Look for “Instructional Videos”.